Abstract
The accuracy and reliability of material parameters obtained through small scale testing are a challenge as testing is limited by the difficulty in sample preparation, its mounting, and alignment. Thus, there is great interest in the development of high throughput testing methodologies, to generate a large amount of data using fewer tests. In a cantilever, in addition to ease of gripping and alignment, the strain gradient along thickness (as well as length) enables the generation of a large volume of data from a single specimen, thereby improving accuracy and reliability. However, the non-linear stress-strain relationship in plasticity leads to redistribution of stress across the cantilever to maintain section planarity. The extraction of flow parameters using a cantilever relies upon the estimation of stress during the deformation. In the present work, a framework is developed to extract strain rate sensitivity from a single cantilever during a deflection rate-controlled test. This demonstrates the effectiveness of bending in reducing the number of tests required to obtain strain rate sensitivity.
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Abbreviations
- E :
-
Young’s modulus
- \({\varepsilon }_{t}\) :
-
Total strain
- \({\varepsilon }_{el}\) :
-
Elastic strain
- \({\varepsilon }_{pl}\) :
-
Plastic strain
- \({\varepsilon }_{t,h}\) :
-
Total strain at distance ‘h’ from the neutral axis
- \({\sigma }_{h}\) :
-
Stress at distance ‘h’ from the neutral axis
- \({\sigma }_{y}\) :
-
Stress at distance ‘y’ from the neutral axis
- \({M}_{x}\) :
-
Moment acting at a distance ‘x’ from the free end
- \(\kappa\) :
-
Curvature of the neutral axis of the beam at any section
- \(F\) :
-
Force
- \(L\) :
-
Length of the cantilever
- \(b\) :
-
Width of the cantilever
- \(h\) :
-
Half-height of the cantilever
- \({l}_{i}\) :
-
Length of ith element
- \({\theta }_{i}\) :
-
Slope of ith element
- \({\delta }_{i}\) :
-
Deflection of ith element
References
Nadai A (1931) Plasticity, 2nd edn. McGraw-Hill Book Company, New York
Tresca HE (1868) Mémoire sur l'écoulement des corps solides. M´em Pres Par Div Sav 18:733–799
de Saint-Venant B (1870) Sur l’etablissement des equations des mouvements interieurs operes dans les corps solides ductiles au-dela des limites ou l’elasticite pourrait les ramener a leur premier etat. Comptes Rendus 70:473–480
Levy M (1870) Mémoire sur les équations générales des mouvements intérieurs des corps solides ductiles au delà des limites où l’élasticité pourrait les ramener à leur premier état. CR Acad Sci Paris 70:1323–1325
Mises RV (1913) Mechanik der festen Körper im plastisch-deformablen Zustand. Nachr Ges Wiss Göttingen Math-Phys Kl 1913:582–592
Prandtl, L.: Spannungsverteilung in plastischen Körpern. In: Proceedings of the 1st international congress on applied mechanics, Delft, pp 43–46 (1924)
Reuss A (1930) Berücksichtigung der elastischen Formänderung in der Plastizitätstheorie. ZAMM-J Appl Math Mech/Z Angew Math Mech 10(3):266–274
Schmidt R (1932) Über den zusammenhang von spannungen und formänderungen im verfestigungsgebiet. Ingenieur-archiv 3(3):215–235
Odqvist FKG (1933) Die verfestigung von flusseisenähnlichen körpern. ein beitrag zur plastizitätstheorie. ZAMM‐Journal Appl Math Mech/Z Angew Math Mech 13(5):360–363
Prager W (1935) Der Einfluß der Verformung auf die Fließbedingung zähplastischer Körper. ZAMM-J Appl Math Mech/Z Angew Math Mech 15(1–2):76–80
Howard JE (1890) Physical properties of iron and steel at high temperature. Iron Age 585
Nadai A, Manjoine MJ (1941) High-speed tension tests at elevated temperatures—parts II and III. J Appl Mech 8:A77
Zener C, Hollomon JH (1944) Effect of strain rate upon plastic flow of steel. J Appl Phys 15(1):22–32
Carreker RP, Hibbard WR (1953) Tensile deformation of high-purity copper as a function of temperature, strain rate, and grain size. Acta Metall 1(6):654–663
Hayden HW, Brophy JH (1968) The interrelation of grain size and superplastic deformation in Ni-Cr-Fe alloys. ASM Trans Q 61(3):542–549 (1968)
Kocks UF (1976) Laws for work-hardening and low-temperature creep. J Eng Mater Technol 98(1):76–85
Johnson AE (1950) A high-sensitivity torsion creep unit. J Sci Instrum 27(3):74–75
Robertson A, Cook G (1913) The transition from the elastic to the plastic state in mild steel. Proc R Soc Lond 88(605):462–471
Prager W (1937) Mécanique des solides isotropes au delà du domaine élastique, vol 87. Gauthier-Villar, Paris
Thum A, Wunderlich F (1932) Die Fließgrenze bei behinderter Formänderung. Forsch Geb Ing A 3(6):261–270
Volterra E, Danusso A, Colonnetti G (1943) Results of experiments on metallic beams bent beyond the elastic limit. J Inst Civ Eng 20(5):1–19
Roderick JW, Phillipps IH (1950) The carrying capacity of simply supported mild steel beams. BWRA
Trifan D (1949) On the plastic bending of circular plates under uniform transverse loads. Q Appl Math 6(4):417–427
Popov EP, Khojasteh-Bakht M, Yaghmai S (1967) Bending of circular plates of hardening material. Int J Solids Struct 3(6):975–988
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Goel, P., Kumar, P., Jayaram, V. (2022). Extracting Strain Rate Sensitivity of Metals from a Single Cantilever Under Bending. In: Jonnalagadda, K., Alankar, A., Balila, N.J., Bhandakkar, T. (eds) Advances in Structural Integrity. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-16-8724-2_32
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